Fundamentals of Deductive Reasoning - Mathematics

Name: Fundamentals of Deductive Reasoning - Mathematics
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Understanding Mathematical Logic, Proofs and Logical Operations

Created byGreat IT Courses

Last updated 10/2019

English

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What you'll learn

Mathematical Statements
Operations on Statements such as "and", "or", contrapositive, Implications, Biconditionals, Converse, etc.
Validating Statements (Identifying Whether a Statement is True or False)

Course content

6 sections • 32 lectures • 16h 35m total length

Instructor Introduction3:21
Course Info and Road Map1:36

Mathematical Statements #129:22
In this video, we'll discuss what criteria a sentence should have so that we can call it a mathematically acceptable statement.
Mathematical Statements #228:39
In this video, we'll discuss what criteria a sentence should have so that we can call it a mathematically acceptable statement.
Exercise 14.134:30
In this video, we will go over the important points of the exercise 14.1 that need to be discussed.

The Negation of a Statement #134:42
Explore the negation of a statement using Boolean algebra and truth values, illustrated with examples like not everyone in Germany speaks German.
The Negation of a Statement #225:00
Master the negation of statements through concrete examples, testing true and false outcomes for rectangles, irrationality of sqrt(7), quadrilaterals, natural numbers, and simple sums.
Compound Statements33:13
learn how compound statements in logic combine two or more statements with connectives like and and or, forming component statements such as P and Q.
Exercise 14.228:31
Explore negation and truth of statements, including universal and existential claims, and analyze compound statements using and/or in the context of boolean algebra and set theory.

"And" as a Connective in Compound Statements32:22
Explore how and functions as a connective in compound statements, true only if both components are true, illustrated with truth tables and basic boolean logic.
“OR” as a Connective in Compound Statements #133:42
In this video, we will talk about “inclusive or” and “Exclusive or”. We will also learn how to check whether a compound statement with “or” is true or false based on whether the component statements are true or false.
“OR” as a Connective in Compound Statements #238:19
In this video, we will talk about “inclusive or” and “Exclusive or”. We will also learn how to check whether a compound statement with “or” is true or false based on whether the component statements are true or false.
Quantifiers25:46
In this video, we will talk about quantifiers like “For Every” and “There Exists”.
Exercise 14.336:25
Explore fundamentals of deductive reasoning by identifying connectives and quantifiers, negating statements, and distinguishing exclusive from inclusive or through practical examples in real numbers and groups.
Implications #132:02
In this video, we will talk about the statement, “If P, then Q”.
Implications #220:27
In this video, we will talk about the statement, “If P, then Q”.
Converse, Contrapositive, Biconditional #129:22
Explore the converse, contrapositive, and biconditional in mathematical logic through if-then statements, truth tables, and geometric examples like isosceles triangles.
Converse, Contrapositive, Biconditional #248:02
Explore converse and contrapositive through p implies q and q implies p, and master biconditional statements with examples, including isosceles triangles and divisibility rules.
Exercise 14.426:18
Explore practice with if-then statements in exercise 14.4: rewrite statements in five forms, identify sufficient and necessary conditions, and apply contrapositive and converse forms to understand logical implication.

Validating Statements #135:51
Validating "And" and "OR" Statements
Validating Statements #242:37
Validating “if-then” and “if-and-only-if” Statements
Validating Statements #332:10
Validation Using the Method of Contradiction
Validating Statements #437:37
Validation Using Contradiction and Counter-example
Exercise 14.4 #136:02
Explore deductive reasoning by applying the direct method, contrapositive, and contradiction to show p implies q for real numbers, detailing assumptions, proofs, and the role of implications.
Exercise 14.4 #228:44
This lecture guides using the contrapositive to prove P implies Q, clarifying the goal, and applying counterexamples to disprove conditional statements while practicing logical reasoning.
Exercise 14.4 #337:13
Explore deductive reasoning by proving statements with the contrapositive, tackling integer and evenness proofs, and using counterexamples to show when implications fail.
Exercise 14.4 #439:36
Examine statements about a circle, radius, diameter, chords, and center, determine true or false with valid reasons, and explore your understanding of ellipses, conic sections, and proofs by contradiction.

Miscellaneous Examples #131:53
Miscellaneous Examples #229:07
Demonstrate necessary and sufficient conditions and p iff q with direct and contrapositive proofs, using odd/even integers and multiples of nine as examples.
Miscellaneous Exercise #138:06
Explore necessary and sufficient conditions, negation of universal and existential statements, and converse and contrapositive, using truth tables and Chapter 14 exercises.
Miscellaneous Exercise #227:53
Delve into deductive reasoning by translating statements into if‑then form, mastering negation, contrapositive, and converse, and exploring necessary and sufficient conditions with prime-number examples.
Miscellaneous Exercise #337:10
Explore forming compound statements with and and or, assess their validity via truth tables, and study proofs by contradiction, including irrational and rational sums.

Requirements

The student must understand basic mathematics all the way up to and including class 11 (Indian Educational System).

Description

In this course, you will learn how to work with mathematical statements, do different operations on them and identify whether they are true or false. We will also talk a little bit about proofs in mathematics here.

This course does not assume much basics so you might "probably" be able to understand the contents of the course if you know basic high school mathematics. However, we are assuming that you know mathematics all the way up to class 11 high school based on the Indian educational system. If you have not gone to school in India and still want to take the course, it is recommended to take a look at our road map in which, all the necessary information regarding your assumed knowledge can be found.

To access the road map, please search for "greatitcourses" on the Internet. Once you get to the website, please read the page titled as, "Mathematics 6-12 Standard".

To locate this particular course in the road map, you can find it under "class 11" with the title, "Mathematical Reasoning".

Thank you!

Who this course is for:

High School Students who are looking to understand basic mathematics in order to use it in higher mathematics, science or engineering

Fundamentals of Deductive Reasoning - Mathematics

What you'll learn

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Course content

Introduction2 lectures • 5min

Mathematical Statements3 lectures • 1hr 33min

Operations on Logical Statements4 lectures • 2hr 1min

Special Words or Phrases10 lectures • 5hr 23min

Validating Statments8 lectures • 4hr 50min

Miscellaneous Exercises5 lectures • 2hr 44min

Requirements

Description

Who this course is for: